{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T06:35:28Z","timestamp":1715409328289},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T00:00:00Z","timestamp":1430352000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that it is complete in the presence of the<jats:italic>\u03c9<\/jats:italic>-rule. By considering this semantics we argue that principles such as introspection, which lead to paradoxical contradictions if naively formulated, should be expressed by using a truth predicate to do the job of quotation and disquotation and observe that in the case of introspection the principle is then consistent.<\/jats:p>","DOI":"10.1017\/s1755020315000118","type":"journal-article","created":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T09:56:51Z","timestamp":1430387811000},"page":"680-704","source":"Crossref","is-referenced-by-count":5,"title":["HOW TO EXPRESS SELF-REFERENTIAL PROBABILITY. A KRIPKEAN PROPOSAL"],"prefix":"10.1017","volume":"8","author":[{"given":"CATRIN","family":"CAMPBELL-MOORE","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,4,30]]},"reference":[{"key":"S1755020315000118_ref22","first-page":"109","volume-title":"Prospects for Pragmatism","author":"Skyrms","year":"1980"},{"key":"S1755020315000118_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF00649483"},{"key":"S1755020315000118_ref15","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.14.3.159"},{"key":"S1755020315000118_ref14","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/fzn030"},{"key":"S1755020315000118_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023080715357"},{"key":"S1755020315000118_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139696586"},{"key":"S1755020315000118_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(90)90060-U"},{"key":"S1755020315000118_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s001820050112"},{"key":"S1755020315000118_ref21","first-page":"1","article-title":"A logic with higher order probabilities","volume":"60","author":"Ognjanovi\u0107","year":"1996","journal-title":"Publications de l\u2019Institut Math\u00e9matique. Nouvelle S\u00e9rie"},{"key":"S1755020315000118_ref26","volume-title":"Oxford Handbook of Probability and Philosophy","author":"Williams","year":"in press"},{"key":"S1755020315000118_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8640.1990.tb00296.x"},{"key":"S1755020315000118_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020308080167"},{"key":"S1755020315000118_ref5","first-page":"13","article-title":"Calibration and probabilism","volume":"1","author":"Caie","year":"2014","journal-title":"Ergo"},{"key":"S1755020315000118_ref16","doi-asserted-by":"publisher","DOI":"10.1006\/game.1999.0788"},{"key":"S1755020315000118_ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020314000069"},{"key":"S1755020315000118_ref11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/978-3-319-09719-0_13","volume-title":"The Life and Work of Leon Henkin","author":"Goldblatt","year":"2014"},{"key":"S1755020315000118_ref10","first-page":"1","article-title":"Axiomatizing semantic theories of truth?","author":"Fischer","year":"2015","journal-title":"The Review of Symbolic Logic, FirstView"},{"key":"S1755020315000118_ref3","volume-title":"Paradox and Belief","author":"Caie","year":"2011"},{"key":"S1755020315000118_ref6","doi-asserted-by":"publisher","DOI":"10.1215\/00318108-2895347"},{"key":"S1755020315000118_ref8","unstructured":"Christiano P. , Yudkowsky E. , Herresho M. , & Barasz M . (n.d.). Definability of Truth in Probabilistic Logic, early draft . Retrieved from https:\/\/intelligence.org\/files\/DefinabilityTruthDraft.pdf (Accessed June 10, 2013)."},{"key":"S1755020315000118_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020314000057"},{"key":"S1755020315000118_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2024634"},{"key":"S1755020315000118_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2013.05.003"},{"key":"S1755020315000118_ref4","doi-asserted-by":"publisher","DOI":"10.1215\/00318108-2315288"},{"key":"S1755020315000118_ref25","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634409"},{"key":"S1755020315000118_ref19","doi-asserted-by":"publisher","DOI":"10.1057\/9781137003720_6"},{"key":"S1755020315000118_ref7","volume-title":"Model Theory","author":"Chang","year":"1990"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020315000118","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T23:00:13Z","timestamp":1691622013000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020315000118\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,30]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["S1755020315000118"],"URL":"https:\/\/doi.org\/10.1017\/s1755020315000118","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,30]]}}}